TSTP Solution File: SEU146+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU146+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 16:22:45 EDT 2023
% Result : Theorem 0.15s 0.50s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 44 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 87 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 30 ~; 39 |; 7 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn; 29 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
subset: ( $i * $i ) > $o ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
singleton: $i > $i ).
tff(decl_27,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
fof(l3_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(l4_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(l2_zfmisc_1,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t3_xboole_1,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(c_0_8,plain,
! [X10,X11,X12] :
( ~ subset(X10,X11)
| in(X12,X10)
| subset(X10,set_difference(X11,singleton(X12))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_zfmisc_1])]) ).
fof(c_0_9,plain,
! [X19,X20] :
( ( set_difference(X19,X20) != empty_set
| subset(X19,X20) )
& ( ~ subset(X19,X20)
| set_difference(X19,X20) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
cnf(c_0_10,plain,
( in(X3,X1)
| subset(X1,set_difference(X2,singleton(X3)))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X17] : subset(X17,X17),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
fof(c_0_14,plain,
! [X8,X9] :
( ( ~ subset(singleton(X8),X9)
| in(X8,X9) )
& ( ~ in(X8,X9)
| subset(singleton(X8),X9) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
cnf(c_0_15,plain,
( subset(X1,empty_set)
| in(X2,X1)
| ~ subset(X3,singleton(X2))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X6,X7] :
( ( subset(X6,X7)
| X6 != X7 )
& ( subset(X7,X6)
| X6 != X7 )
& ( ~ subset(X6,X7)
| ~ subset(X7,X6)
| X6 = X7 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(c_0_18,negated_conjecture,
( ( esk1_0 != empty_set
| ~ subset(esk1_0,singleton(esk2_0)) )
& ( esk1_0 != singleton(esk2_0)
| ~ subset(esk1_0,singleton(esk2_0)) )
& ( subset(esk1_0,singleton(esk2_0))
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_19,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( subset(X1,empty_set)
| in(X2,X1)
| ~ subset(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,plain,
! [X21] :
( ~ subset(X21,empty_set)
| X21 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
cnf(c_0_22,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( subset(esk1_0,singleton(esk2_0))
| esk1_0 = empty_set
| esk1_0 = singleton(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( subset(singleton(X1),X2)
| subset(X2,empty_set)
| ~ subset(X2,singleton(X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( singleton(esk2_0) = esk1_0
| esk1_0 = empty_set
| ~ subset(singleton(esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( esk1_0 != singleton(esk2_0)
| ~ subset(esk1_0,singleton(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( singleton(esk2_0) = esk1_0
| esk1_0 = empty_set ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_25]),c_0_26]) ).
fof(c_0_29,plain,
! [X18] : subset(empty_set,X18),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_30,negated_conjecture,
( esk1_0 != empty_set
| ~ subset(esk1_0,singleton(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
esk1_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16])]) ).
cnf(c_0_32,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU146+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Wed Aug 23 13:06:56 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.15/0.49 start to proof: theBenchmark
% 0.15/0.50 % Version : CSE_E---1.5
% 0.15/0.50 % Problem : theBenchmark.p
% 0.15/0.50 % Proof found
% 0.15/0.50 % SZS status Theorem for theBenchmark.p
% 0.15/0.50 % SZS output start Proof
% See solution above
% 0.15/0.51 % Total time : 0.008000 s
% 0.15/0.51 % SZS output end Proof
% 0.15/0.51 % Total time : 0.010000 s
%------------------------------------------------------------------------------